Difference Between Normalizer, Centralizer, and Stabilizer
An easy way to remember what is the normalizer and centralizer of a subgroup, and what is the stabilizer of an element under a group action. For people learning abstract algebra! Group Theory playlist: https://youtube.com/playlist?list=PLug5ZIRrShJHDvvls4OtoBHi6cNnTZ6a6 Subscribe to see
From playlist Group Theory
This lecture is part of an online math course on group theory. We review free abelian groups, then construct free (non-abelian) groups, and show that they are given by the set of reduced words, and as a bonus find that they are residually finite.
From playlist Group theory
Galois theory: Algebraic closure
This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically
From playlist Galois theory
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
Field Theory - Algebraically Closed Fields (part 2) - Lecture 10
In this video we should that algebraically closed fields exist and are unique. We assume that the direct limit construction works. The construction here depends on the axiom of choice.
From playlist Field Theory
Group theory 32: Subgroups of free groups
This lecture is part of an online mathematics course on group theory. We describe subgroups of free groups, show that they are free, calculate the number of generators, and give two examples.
From playlist Group theory
Commutative Algebra - Integral Closures - part 01 - Basics
This is a video for a second semester graduate algebra class.
From playlist Integral Closures
Group theory 21: Groups of order 24
This lecture is part of an online mathematics course on groups theory. It gives a survey of the groups of order 24, and discusses two of them (the symmetric group and the binary tetrahedral group) in more detail.
From playlist Group theory
Matrix Theory: Consider the set G of matrices of the form [x y \ 1 0] where x is nonzero real and y is real. Let G act on the real line R by [x y \ 1 0].t = xt + y. Show that G is a group, that the action is a group action, and that the action is faithful.
From playlist Matrix Theory
Title: Interpretations and Differential Galois Extensions
From playlist Fall 2014
Richard Hain: Mixed motives associated to elliptic curves
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Galois theory: Normal extensions
This lecture is part of an online graduate course on Galois theory. We define normal extensions of fields by three equivalent conditions, and give some examples of normal and non-normal extensions. In particular we show that a normal extension of a normal extension need not be normal.
From playlist Galois theory
Samaria Montenegro, Universidad de Costa Rica
November 11, Samaria Montenegro, Universidad de Costa Rica Title: Groups definable in partial differential fields with an automorphism
From playlist Fall 2021 Online Kolchin Seminar in Differential Algebra
Reid Dale Talk 2 9/16/16 Part 1
Title: An Introduction to Pillay’s Differential Galois Theory (Part 2)
From playlist Fall 2016
Galois theory: Galois extensions
This lecture is part of an online graduate course on Galois theory. We define Galois extensions in 5 different ways, and show that 4 f these conditions are equivalent. (The 5th equivalence will be proved in a later lecture.) We use this to show that any finite group is the Galois group of
From playlist Galois theory
Kevin Buzzard (lecture 2/20) Automorphic Forms And The Langlands Program [2017]
Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w
From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]
New isolated symplectic singularities with trivial fundamental group - Daniel Juteau
Workshop on Representation Theory and Geometry Topic: New isolated symplectic singularities with trivial fundamental group Speaker: Daniel Juteau Affiliation: CNRS, Université Paris Diderot; Member, School of Mathematics Date: March 31, 2021 For more video please visit http://video.ias.e
From playlist Mathematics
Galois theory: Separable extensions
This lecture is part of an online graduate course on Galois theory. We define separable algebraic extensions, and give some examples of separable and non-separable extensions. At the end we briefly discuss purely inseparable extensions.
From playlist Galois theory
Lie Groups and Lie Algebras: Lesson 43 Group Theory Review #2 (improved video quality)
Lie Groups and Lie Algebras: Lesson 43 Group Theory Review #2 In this lecture we examine a great way of becoming familiar with the smaller groups: the subgroup lattice. We use this to remind ourselves about normal subgroups, cyclic subgroups, and the center of a group. Errata!: The norma
From playlist Lie Groups and Lie Algebras
Polynomial Identity Testing via Optimization: algorithms by Rafael Oliveira
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019